标题： 理论/数值研究抑制稳定网络中的调制行波 显示英文标题

标题： Theoretical / numerical study of modulated traveling waves in inhibition stabilized networks

摘要： 我们证明了关于实线上神经场方程的行波解的线性化稳定性原理。 此外，我们提供了接近行波的有限维不变中心流形的存在性，这使得可以研究行波的分岔。 最后，研究了调制行波的谱性质。 提供了计算调制行波的数值方案。 然后我们将这些结果和方法应用于研究一个处于抑制稳定状态下的神经场模型。 我们展示了行波脉冲的折叠、霍普夫和博德加诺夫-塔肯斯分岔。 此外，我们将调制行波脉冲作为两个神经种群的时间尺度比的函数进行延续，并展示了调制行波脉冲蛇形行为的数值证据。 显示英文摘要

摘要： We prove a principle of linearized stability for traveling wave solutions to neural field equations posed on the real line. Additionally, we provide the existence of a finite dimensional invariant center manifold close to a traveling wave, this allows to study bifurcations of traveling waves. Finally, the spectral properties of the modulated traveling waves are investigated. Numerical schemes for the computation of modulated traveling waves are provided. We then apply these results and methods to study a neural field model in a inhibitory stabilized regime. We showcase Fold, Hopf and Bodgdanov-Takens bifurcations of traveling pulses. Additionally, we continue the modulated traveling pulses as function of the time scale ratio of the two neural populations and show numerical evidences for snaking of modulated traveling pulses.